take someone at his or her word
Also, take someone's word for. Accept what someone says on trust, as in Since he said he'd agree to any of my ideas, I'll take him at his word, or She said she wanted to help out and I took her word for it. This idiom appeared in Miles Coverdale's translation of the Bible: "He said ... he is my brother. And the men took him shortly at his word" (I Kings 22:33). It is still so used.